Find the Volume of the Solid Generated by Revolving the Region

question 16

Multiple Choice

Find the volume of the solid generated by revolving the region about the given line.
-The region bounded above by the line $y = 16$ , below by the curve $y = 16 - x ^ { 2 }$ , and on the right by the line $x = 4$ , about the line $y = 16$

• A) \(\frac { 8192 } { 15 } \pi\)
• B) \(\frac { 1024 } { 5 } \pi\)
• C) \(\frac { 64 } { 3 } \pi\)
• D) \(\frac { 7168 } { 15 } \pi\)

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Definitions:

Progressive Income Tax

A tax system where the tax rate increases as the taxable income of the taxpayer increases, aiming at a more equitable distribution of wealth.

After-Tax Lorenz Curve

A graphical representation that shows the distribution of income or wealth within an economy after accounting for taxes.

Before-Tax Lorenz Curve

A graphical representation that shows the distribution of income or wealth among individuals or households before taxes are applied.

Lorenz Curve

A graphical representation of income or wealth distribution within a society, showing the proportion of overall income earned by cumulative percentages of the population.